The main goal of the paper is to show the application of the projection method as a tool for the analysis of transitional dynamics of endogenous growth models, the analysis which is very often omitted in common literature on the topic. The application of the method is demonstrated on an endogenous growth model with human capital accumulation and government sector. We analyze the long-run (steady states) and the short-run effects (transitional dynamics) of different fiscal policies. The transitional dynamics of the competitive equilibrium and the social optimum economies are compared. It is shown that when the economy starts with relatively abundant physical capital it is optimal to decrease its level very rapidly even at the cost of a big decline of consumption for a period of time. The introduction of education subsidies can bring the economy closer to the optimum and, therefore, improve the welfare of the society.